1. Field of the Invention
This invention relates to cyclohexane derivatives which are liquid crystalline compounds suitable as a component in a liquid crystal composition, liquid crystal compositions comprising the same and liquid crystal display devices composed of these liquid crystal compositions.
2. Description of Related Art
A liquid crystal display device utilizing an optical anisotoropy and a dielectric anisotropy of a liquid crystal substance is classified into a twisted nematic type (TN type), a super twisted nematic type (STN type), a dynamic scattering type (DS type), a guest-host type (G-H type) and DAP type, in view of a display system. It is also classified into a static drive system, a time rate drive system, an active matrix drive system and 2 cycle drive system, in view of a drive system. Various liquid crystal substances having different properties depending on their application are used for these liquid crystal display devices. As a common property, any liquid crystal substance needs to have a stability to external environmental factors such as moisture, air, heat and light, to exhibit liquid crystal phase within as broad the temperature range as possible focusing on room temperature, to have low viscosity and to make the driving voltage low when the display device is driven. Further, it needs to have the characteristics desired according to each display device, for example, the optimum dielectric anisotropy (xcex94xcex5) and the optimum optical anisotropy (xcex94n).
However, there is no substance which meets such all requirements with a single compound now. The present condition is mixing several to about twenty sorts of liquid crystalline compounds to prepare a liquid crystal composition and using the composition as liquid crystal material. The term xe2x80x9cliquid crystalline compoundxe2x80x9d as used herein refers generically to a compound having a liquid crystal phase and a compound not impairing a liquid crystal phase when mixed with other liquid crystal compounds.
Therefore, it is desirable that liquid crystalline compounds used as a component in the composition have good compatibility each other and also they have good compatibility even at a cryostatic temperature, since the demand to the use under various environment is increasing recently.
In recent years, liquid crystal display device is required with higher quality, especially in a display performance, for example, contrast, display capacity, response time, etc. To meet the requirement, the demand for the display device of an active matrix system represented by a TFT (thin film transistor) system is increasing in display mode fields, mainly television and a view finder.
The display device of STN system has been often used in the display fields such as a pocket phone and a personal computer, because of its low cost, easy manufacturing process while having large display capacity.
The development tendency in recent years in these fields is advanced focusing on a downsizing and portability of a liquid crystal display device as observed in the television and note type personal computer which are portable by downsizing and light saving. The liquid crystal material used in connection with this requires a liquid crystalline compound of low driving voltage, i.e., those capable of providing reduced threshold voltage, and a liquid crystal composition of low driving voltage comprising the same.
The threshold voltage (Vth) is shown by the following formula as known well (H. J. Deuling, et al., Mol. Cryst. Liq. Cryst., 27 (1975) 81).
Vth=xcex7(K/xcex50xcex94xcex5)xc2xd in which K is an elastic constant of liquid crystal material and xcex50 is a dielectric constant in a vacuum. As seen from the above formula, two ways can be considered whether xcex94xcex5 is increased or K is decreased, in order to reduce Vth. However, with the present technology, it is still difficult to control the elastic constant K of liquid crystal material actually. Under the present circumstances, one complies with a demand by using a liquid crystal material of large xcex94xcex5. For such circumstances, liquid crystalline compounds of large xcex94xcex5 have been developed actively.
At present, most liquid crystal compositions used for the display device of TFT system are composed of fluorine-containing liquid crystal materials. The reason is that the display device of TFT system requires the liquid crystal composition capable of providing high voltage holding rate (V.H.R) under low temperature dependence, but there is no other liquid crystalline compound except for fluorine-containing compounds to meet such requirements.
To increase xcex94xcex5 in the liquid crystalline compound, it is effective to maintain a substituent having large dipole moment such as cyano and trifluoromethyl in the terminal group as well known, or to replace 1,4-phenylene in the compound by halogen such as fluorine, so that the direction of a dipole moment may become identical with that of the terminal substituent. However, it has been considered to be difficult to increase only xcex94xcex5, while controlling both an increase in viscosity and a reduction in the temperature range of a liquid crystal phase, since the number of replaced fluorine atom is proportional to the viscosity and the number of replaced fluorine atom is increased with reducing the temperature range of a liquid crystal phase.
In recent years, development of the liquid crystal display, especially using a reflected type TFT system is also active. For this reflected type liquid crystal display, a compound of low xcex94n is required.
As compounds already reported, U.S. Pat. No. 4,797,228 discloses the compound of the following formula (A) and Japanese Patent Kokai 2-233626 discloses the compound of the following formula (B). 
in which R represents a straight-chain alkyl.
Among these, the compound of formula (A) is reported to be comparatively stable and highly reliable. However, xcex94xcex5 of the compound (A) is comparatively as small as about 3-5 and also xcex94xcex5 of the liquid crystal composition consisting of only the same is small, which cannot reduce the driving voltage. To make up for this defect, the compound of formula (B) was developed. This compound had large xcex94xcex5 and low viscosity, and could reduce the driving voltage without increasing the viscosity of the liquid crystal composition.
Accordingly, it has been desired to develop a liquid crystal material of large xcex94xcex5 without reducing the liquid crystal phase temperature range, and further of small xcex94n and high stability.
An object of the present invention is to provide a new liquid crystalline compound having large xcex94xcex5 and relatively low viscosity which can overcome the defects of the prior art as mentioned above, a liquid crystal composition comprising said liquid crystalline compound and a liquid crystal display device composed of said liquid crystal composition.
We have investigated various compounds in an effort to solve the aforesaid problems and found new liquid crystalline compounds having more improved characteristics than known liquid crystalline compounds, thus leading to the completion of the present invention.
In the first aspect, the present invention relates to a liquid crystalline compound represented by formula (1) 
wherein R1 represents hydrogen or C1-C15 alkyl in which one or more non-adjacent methylene may be replaced by oxygen, sulfur or xe2x80x94CHxe2x95x90CHxe2x80x94 and one or more hydrogen may be replaced by halogen; R2 represents hydrogen, cyano, halogen or C1-C15 alkyl in which one or more non-adjacent methylene may be replaced by oxygen, sulfur or xe2x80x94CHxe2x95x90CHxe2x80x94 and one or more hydrogen may be replaced by halogen; L represents halogen or hydrogen; A1, A2, A4 and A5 each independently represent trans-1,4-cyclohexylene or 1,4-phenylene, one or more xe2x80x94CH2xe2x80x94 in the trans-1,4-cyclohexylene may be replaced by oxygen or sulfur, one or more xe2x95x90CHxe2x80x94 in the 1,4-phenylene may be replaced by nitrogen, and one or more hydrogen in the 1,4-phenylene ring may be replaced by halogen; A3represents trans-1,4-cyclohexylene in which one or more xe2x80x94CH2xe2x80x94 may be replaced by oxygen or sulfur; Z1,Z2,Z3 and Z4each independently represent xe2x80x94COOxe2x80x94, xe2x80x94OCOxe2x80x94, xe2x80x94CH2CH2xe2x80x94, xe2x80x94(CH2)4xe2x80x94, CH2Oxe2x80x94, xe2x80x94OCH2xe2x80x94, xe2x80x94CF2Oxe2x80x94, xe2x80x94OCF2xe2x80x94 or a single bond; Q represents xe2x80x94CF2CH2xe2x80x94 or xe2x80x94CH2CF2xe2x80x94; and k, l, m and n each independently represent 0 or 1 with the condition of k+l+m+nxe2x89xa62.
The embodiments of the present compounds include the following cases in formula (1):
k=l=m=n=0,
k+l=1 and m=n=0,
k=l=0 and m+n=1,
k+l=1 and m+n=1,
k=l=0 and m=n=1,
A3 is trans-1,4-cyclohexylene,
R2 is fluorine,
A3is trans-1,4-cyclohexylene and R2is fluorine,
k+l =1, m=n=0, A1 or A2 is trans-1,4-cyclohexylene, A3 is trans-1,4-cyclohexylene, and Z1 or Z2is a single bond, or
k+l=1, m=n=0, A1 or A2 is trans-1,4-cyclohexylene, A3 is trans-1,4-cyclohexylene, Z1 or Z2is a single bond,
and R2and L is fluorine.
In the second aspect, the present invention relates to a liquid crystal composition which comprises at least one liquid crystalline compound represented by formula (1). In one embodiment of the present second invention, the liquid crystal composition may further comprise as a second component at least one compound selected from the group consisting of the compound of formula (2), the compound of formula (3) or the compound of formula (4) 
wherein R3, Y1, La, Lb, Z5and Z6 may be identical or different between each formula; R3represents C1-C10 alkyl in which one or more non-adjacent methylene may be replaced by oxygen or xe2x80x94CHxe2x95x90CHxe2x80x94 and any hydrogen may be replaced by fluorine; Y1 represents fluorine, chlorine, OCF3OCHF2, CF3, CHF2, CH2F, OCF2CHF2or OCF2CHF CF3; La and Lb each independently represent hydrogen or fluorine; Z5 and Z6each independently represent xe2x80x94CH2CH2xe2x80x94, xe2x80x94(CH2)4xe2x80x94, xe2x80x94COOxe2x80x94, xe2x80x94CF2Oxe2x80x94, xe2x80x94OCF2xe2x80x94, xe2x80x94CHxe2x95x90CHxe2x80x94 or a single bond; six-membered ring B represents trans-1,4-cyclohexylene, 1,3-dioxane-2,5-diyl or 1,4-phenylene in which hydrogen may be replaced by fluorine; six-membered ring C represents trans-1,4-cyclohexylene or 1,4-phenylene in which hydrogen may be replaced by fluorine; and in the above compound of each formula, each atom constituting the compound may include its isotope.
In another embodiment of the second invention, the liquid crystal composition may further comprise as a second component at least one compound selected from the group consisting of the compound of formula (5) or the compound of formula (6) 
wherein R4and R5 each independently represent C1-C10 alkyl in which one or more non-adjacent methylene may be replaced by oxygen or xe2x80x94CHxe2x95x90CHxe2x80x94 and any hydrogen may be replaced by fluorine; Y2represents xe2x80x94CN or xe2x80x94Cxe2x89xa1Cxe2x80x94CN; six-membered ring E represents trans-1,4-cyclohexylene, 1,4-phenylene, 1,3-dioxane-2,5-diyl or pyrimidine-2,5-diyl; six-membered ring G represents trans-1,4-cyclohexylene, 1,4-phenylene in which hydrogen may be replaced by fluorine or pyrimidine-2,5-diyl; six-membered ring H represents trans-1,4-cyclohexylene or 1,4-phenylene; Z7 represents xe2x80x94CH2CH2xe2x80x94, xe2x80x94COOxe2x80x94 or a single bond; Lc, Ld and Le each independently represent hydrogen or fluorine; b, c and d each independently represent 0 or 1; and in the above compound of each formula, each atom constituting the compound may include its isotope.
In further embodiment of the second invention, the liquid crystal composition may further comprise as a second component at least one compound selected from the group consisting of the compound of formula (2), the compound of formula (3) and the compound of formula (4) and as a third component at least one compound selected from the group consisting of the compound of formula (7), the compound of formula (8) and the compound of formula (9)
R6xe2x80x94(I)xe2x80x94Z8xe2x80x94(J)xe2x80x94Z9xe2x80x94R7xe2x80x83xe2x80x83(7)
R6xe2x80x94(I)xe2x80x94Z8xe2x80x94(J)xe2x80x94Z9xe2x80x94(K)xe2x80x94R7xe2x80x83xe2x80x83(8)

wherein R6, R7, I, J and K may be identical or different between each formula; R6 and R7 each independently represent C1-C10 alkyl in which one or more non-adjacent methylene may be replaced by oxygen or xe2x80x94CHxe2x95x90CHxe2x80x94 and any hydrogen may be replaced by fluorine; I, J and K each independently trans-1,4-cyclohexylene, pyrimidine-2,5-diyl or 1,4-phenylene in which hydrogen may be replaced by fluorine; Z8 and Z9 each independently represent xe2x80x94Cxe2x89xa1Cxe2x80x94, xe2x80x94COOxe2x80x94, xe2x80x94CH2CH2xe2x80x94, xe2x80x94CHxe2x95x90CHxe2x80x94 or a single bond, and in the above compound of each formula, each atom constituting the compound may include its isotope.
In further embodiment of the second invention, the liquid crystal composition may further comprise as a second component at least one compound selected from the group consisting of the compound of formula (5) or the compound of formula (6) and as a third component at least one compound selected from the group consisting of the compound of formula (7), the compound of formula (8) or the compound of formula (9).
In further embodiment of the second invention, the liquid crystal composition may further comprise as a second component at least one compound selected from the group consisting of the compound of formula (2), the compound of formula (3) or the compound of formula (4) and as a third component at least one compounds selected from the group consisting of the compound of formula (5) or the compound of formula (6), and as a fourth component at least one compound selected from the group consisting of the compound of formula (7), the compound of formula (8) or the compound of formula (9).
In still further embodiment of the second invention, the liquid crystal compositions as recited above may further contain any optically active compound.
In the third aspect, the present invention relates to a liquid crystal display device composed of any of the present liquid crystal compositions as recited above.
The liquid crystalline compounds of the present invention represented by formula (1) have a partial structure comprising 1,1-difluoroethylene and exhibit excellent characteristics, especially low xcex94n and large xcex94xcex5 as described later by a synergistic effect of the halogen atom or the like substituted on 1,4-phenylene ring.
The compounds of formula (1) are specified by those represented by the following formulae (1a) to (1f). 
In these formulae, A1, A2, A3, A4, A5, L, R1, R2, Q, Z1, Z2, Z3 and Z4 represent the same meanings as described above.
Of these specific compounds, the dicyclic compound of formula (1a) (k=l=m=n=0) has large xcex94xcex5, relatively small xcex94n, low viscosity and good compatibility at low temperature. This compound can provide a composition for high-speed response when used as a component of the liquid crystal composition, since it can reduce the viscosity while maintaining xcex94xcex5 of the composition.
The tricyclic compounds, i.e., the compound of formula (1b) (k=1 and l=m=n=0) and the compound of formula (1c) (k=l=n=0 and m=1) and the tetracyclic compounds, i.e., the compound of formula (1d) (k=m=1 and l=n=0) or the compound of formula (1e) (k=l=0 and m=n=1) have large xcex94xcex5, relatively low viscosity and relatively broad temperature range of liquid phase. These compounds are useful for expanding the liquid phase temperature range to a high temperature side while maintaining the dielectric anisotropy of the resulting composition, when used as a component of the liquid crystal composition.
Of the compounds as specifically recited above, preferable examples of the compounds included in those of formula (1b) are more specifically recited by the compounds of the following formulas (1b-1) to (1b-16). Preferable examples of the compounds included in those of formula (1c) are more specifically recited by the compounds of the following formulas (1c-1) to (1c-22). Preferable examples of the compounds included in those of formula (1d) are more specifically recited by the compounds of the following formulas (1d-1) to (1d-20). Preferable examples of the compounds included in those of formula (1e) are more specifically recited by the compounds of the following formulas (1e-l) to (1e-20). Preferable examples of the compounds included in those of formula (1f) are more specifically recited by the compounds of the following formulas (1f-1) to (1f-18). 
In the above formulas, R1, R2 and L represent the same meaning as mentioned above, and one or more halogen atoms may be replaced on 1,4-phenylene ring.
Of these compounds as more specifically recited above, the compound of formula (1b-1) especially replaced by fluorine provides larger xcex94xcex5 with the increase in the replacement number of fluorine, and further improves the compatibility at low temperature.
The compound of formula (1b-9) wherein L is fluorine and R2 is trifluoromethoxy exhibits large xcex94xcex5 and also improves the compatibility at low temperature.
The liquid crystal composition of the present invention contains at least one of the liquid crystalline compounds represented by formula (1) as a first component. The content of said compound is required to be at least 1% based on the weight of the liquid crystal composition to produce excellent characteristics. Preferred mixing percentage of the first component is 1-50% by weight, more preferably 3-20% by weight.
The liquid crystal compositions of the present invention may be (I) the composition comprising only the first component as mentioned above, but preferably (II) the composition wherein at least one compound selected from the group consisting of the compounds of formulas (2), (3) and (4) is mixed as the second component in addition to the first component; (III) the composition wherein the composition (I) is mixed with at least one compound selected from the group consisting of the compounds of formulas (5) and (6) as the second component; (IV) the composition wherein the composition (II) is mixed with at least one compound selected from the group consisting of the compounds of formulas (7), (8) and (9) as the third component; (V) the composition wherein the composition (III) is mixed with at least one compound selected from the group consisting of the compounds of formulas (7), (8) and (9) as the third component; and (VI) the composition wherein the composition (II) is mixed with at least one compound selected from the group consisting of the compounds of formulas (5) and (6) as the third component and further at least one compound selected from the group consisting of the compounds of formulas (7), (8) and (9) as the fourth component. Further, other components can be mixed suitably. For example, an optically active compound may be added as a helical pitch modifier, and known compounds may be mixed for the purpose of regulating threshold voltage, liquid crystal temperature range, xcex94n, xcex94xcex5, viscosity and the like.
Of the second components as mentioned above, suitable examples of the compounds included in the formula (2) can include those represented by the following formulas (2-1) to (2-9). Suitable examples of the compounds included in the formula (3) can include those represented by the following formulas (3-1) to (3-63). Suitable examples of the compounds included in the formula (4) can include those represented by the following formulas (4-1) to (4-15). 
In the above formulas, R3 and Y1 have the meanings as mentioned above.
Of these compounds, the compounds of formulas (2) to (4) have positive xcex94xcex5, excellent thermal and chemical stability, which are useful in the preparation of the liquid crystal composition for TFT which requires high reliability such as high voltage holding rate (large specific resistance).
The mixing percentage of said compounds in the present composition is at least 1% by weight, preferably 10-97% by weight, more preferably 40-95% by weight based on the total weight of the liquid crystal composition, when the liquid crystal composition for TFT is prepared. In that case, the compounds of formulas (7) to (9) may be incorporated.
The compounds of formulas (2) to (4) can be also used in the preparation of liquid crystal composition for STN and TN display mode which drive at low voltage. Preferably, the amount of the compound used in this case is 50% by weight or less based on the total weight of the liquid crystal composition.
Of the compounds as recited above, suitable examples of the compounds included in the formula (5) can include those of the following formulas (5-1) to (5-40), and suitable examples of the compounds included in the formula (6) can include those of the following formulas (6-1) to (6-3). 
In the above formulae, R4, R5 and Y2 have the meanings as mentioned above.
The compounds of formula (5) or (6) have positive xcex94xcex5 and its large value., and they are used for the purpose of reducing the threshold voltage of the device composed of the resulting composition. Further, these compounds are used for the purpose of improving the steepness in electro-optical characteristic curve, regulating xcex94n and increasing a clear point to broaden a nematic phase range, and they are especially suitable in the preparation of liquid crystal composition for liquid display device driving at low voltage.
These compounds can make the threshold voltage of the liquid crystal composition lower according to an increase in the amount of the compound used, but bringing about an increase in viscosity. As long as the viscosity of the liquid crystal composition satisfies the required physical value, larger amount of the compound used is advantageous from a viewpoint of the driving at low voltage.
Under such circumstances, the amount of the above compound used is at least 1% by weight based on the total weight of the liquid crystal composition, preferably 10-97% by weight, more preferably 40-95% by weight of the resulting composition. Of the compounds as recited above, suitable examples of the compounds included in the formula (7) can include those of the following formulas (7-1) to (7-11), suitable examples of the compounds included in the formula (8) can include those of the following formulas (8-1) to (8-18), and suitable examples of the compounds included in the formula (9) can include those of the following formulas (9-1) to (9-6). 
In the above formulas, R6 and R7 have the same meanings as mentioned above.
The compounds of formulas (7) to (9) are small and close to zero in the absolute value of xcex94xcex5. Of these compounds, the compound of formula (7) is used mainly for the adjustment of viscosity or xcex94n of the resulting liquid crystal composition. The compounds of formulas (8) and (9) are used for increasing a clear point of the resulting composition to broaden a nematic phase range of the composition or adjusting xcex94n.
These compounds can make the threshold voltage of the liquid crystal composition higher according to an increase in the amount of the compound used, but reducing the viscosity. As long as the threshold voltage of the liquid crystal composition satisfies the required physical value, larger amount of the compound used is desirable.
Under such circumstances, suitable amount of the above compound used is not more than 40% by weight, preferably not more than 35% by weight based on the total weight of the liquid crystal composition, when high reliability is required as in the liquid crystal composition for TFT. When low threshold voltage is required as in the liquid crystal composition for STN and TN display modes, suitable amount of the above compound used is not more than 70% by weight, preferably not more than 60% by weight based on the total weight of the liquid crystal composition.
Of other components in the composition of the present invention, an optically active compound is added for the purpose of causing a helical structure of liquid crystal composition to adjust necessary twist angle, thereby preventing a reverse twist, except for a special case, for example the case where the component is used in the liquid crystal composition for OCB (Optically Compensated Birefringence) mode.
The optically active compound is extensively selected from known compounds as far as the above purpose is achieved. Preferable examples of optically active compounds can include those of the following formulas (Op-1) to (Op-8). 
By addition of these optically active compounds, the pitch length of twist in the resulting liquid crystal composition is adjusted. Preferably, the pitch length of twist is adjusted in the range of 6 to 20 xcexcm for the liquid crystal composition for STN and in the range of 1.5 to 4 xcexcm for the composition for bistable TN mode. In that case, two or more optically active compounds may be added for the purpose of adjusting a temperature dependence of pitch length.
The liquid crystal composition of the present invention can be used in the display device of either field-effect or current-effect type. For Example, it can be used in the display devices of a twisted nematic mode, a twisted nematic mode in combination with an active matrix system, a supertwisted nematic mode and a field-controlled birefringent mode. Further, the present composition can be used as a liquid crystal composition for guest-host (GH) mode by incorporating therein diachronic dyes such as merocyanines, styryls, azo, azomethines, azoxy, quinophthalones, anthraquinones, tetrazines or the like. In addition, it can be used in the display devices which include a device wherein an encapsulated liquid crystal composition is dispersed in a polymer and a device wherein a liquid crystal composition is present in a spongy polymer.
The compounds of the present invention represented by formula (1) can be prepared by selecting usual methods in a synthetic organic chemistry and combining them. For example, methods described in xe2x80x9cOrganic Synthesisxe2x80x9d (John Wiley and Sons, Inc.), xe2x80x9cOrganic Reactionsxe2x80x9d (John Wiley and Sons, Inc.), xe2x80x9cJitsuken Kagaku Kouzaxe2x80x9d (Maruzen Co. Ltd.) or the like may be selected suitably and combined.
For example, Wittig reagent (10) described in xe2x80x9cOrganic Reactions, vol. 14, page 270xe2x80x9d and a ylid compound prepared from a base such as potassium-t-butoxide and alkyl lithium are reacted with cyclohexanone derivative (11) to prepare olefin derivative (12). Subsequently, olefin derivative (12) is reacted with 9-borabicyclo[3.3.1]nonane (abbreviated hereafter as 9-BBN), and followed by oxidation to prepare alcohol derivative (13) which is then converted to ketone derivative (14), for example by Swern oxidation described in xe2x80x9cJitsuken Kagaku Kouzaxe2x80x9d, 4 edn. Vol. 23, page 299. The ketone (14) can be fluorinated with diethylaminosulfurtrifluoride (abbreviated hereafter as xe2x80x9cDASTxe2x80x9d) to prepare a target compound of formula (1) (See, the following Scheme 1);
Alternatively, Grignard reagent prepared from alkyl halide derivative (15) is reacted with aldehyde derivative (16) to prepare alcohol derivative (17) which can be then oxidized and fluorinated in the same manner as mentioned above to prepare a target compound of formula (1) (See, the following Scheme 2). 
In the above formulas, A1, A2, A4, A5, R1, R2, Z1, Z2, Z3, Z4, L, k, l, m and n have the same meanings as mentioned above. Of starting materials as mentioned above, Wittig reagent (10) and alkyl halide derivative (15) can be prepared suitably by the following methods.
Aldehyde derivative (16) is reacted with a ylid compound prepared from methoxymethyltriphenylphosphonium chloride and potassium-t-butoxide to prepare olefin derivative (19). This derivative is hydrolyzed to aldehyde derivative (20) which is then reduced to alcohol derivative (21). This derivative can be halogenated to alkyl halide derivative (22), thus leading to Wittig reagent (10)(See, the following Scheme 3).
Olefin derivative (23) is prepared from cyclohexanone derivative (11) in accordance with conventional method. Olefin derivative (23) is hydrolyzed with an acid such as hydrochloric acid to aldehyde derivative (24) which is then reduced with sodium borohydride to alcohol derivative (25). This derivative can be halogenated with hydrobromic acid to alkyl halide derivative (15-1)(See, the following Scheme 4). 
In the above formulas, A1, A2, A4, A5, L, Z1, Z2, Z3, Z4 R1 R2, k, l, m and n have the same meanings as mentioned above.